Composition of Functions
Composition vs. Multiplication
Notice in the two previous symbolic examples, the resulting composite functions are not the same.
( f o g)(x) = –2x2 + 13
(g o f )(x) = –4x2 – 12x – 4
In general (f o g)(x) is not the same as (g o f )(x). In particular, composition is not the same as multiplication. The open dot is not the same as a multiplication dot, nor does it mean the same thing. While the following is true:
f (x) • g(x) = g(x) • f(x) [Commutative Property of Multiplication]
...you cannot say that:
(f o g)(x) = (g o f)(x) [generally false for composition]
Composition is not commutative like multiplication, and is an entirely different process.